Testing a hybrid Coulomb/statistical model of aftershock occurrence

The Sichuan earthquake in mid-May killed more than 87,000 persons and caused damage on the order of fifty billion pounds. Much of the damage, and further loss of life, resulted from aftershocks - smaller earthquakes triggered by the occurrence of the M7.9 mainshock. Research over the past 15 years or so has increased our understanding of aftershocks and particularly of the controls on their locations. The most important realisation is that large earthquakes induce stress changes in the surrounding crust which can be calculated within a few hours of the mainshock; areas of stress increase correlate strongly with the occurrence of aftershocks. (These 'Coulomb' stresses are computed by resolving the tensorial stress perturbation into shear and normal components on planes of interest; increased shear stress and decrease normal stress encourage failure.) Maps of such stress changes can be used to inform emergency response so that, for example, evacuation shelters are sited in areas where stress has decreased and hence aftershocks are not expected. More useful information for emergency services would be an estimation of the probability of an earthquake above a particular magnitude affecting any given location. Calculating such probabilities is not straight-forward, however, as the only model that directly relates stress and probability changes is based on laboratory friction experiments and relies on a number of assumptions that may not be realistic as well as the determination of a number of poorly constrained parameters. To date, this model has only been subjected to one systematic test and the results were inconclusive. An alternative approach to estimating aftershock probabilities is purely statistical, based on two key observations: the Gutenberg-Richter relation which describes the number-size distribution of earthquakes and the Omori law for decrease in aftershock numbers with time. In a recent test on a single aftershock sequence, the abilities of 7 statistical and 4 stress-based models to forecast probabilities were rigorously tested. Surprisingly, the statistical models fared best, despite their lack of the essential physics that controls the spatial distribution of aftershocks. The reason for this result is open to interpretation, but the stress-based models may have suffered because of the failure of the unphysical assumptions in the friction law or because the required parameters were not estimated correctly. Alternatively, because in this model the expected rate of aftershocks depends on the magnitude of the stress change, there may have been problems with the calculated stress field due to un-modelled small scale heterogeneity in the earthquake slip distribution. The aim of this project is to develop a combined stress/statistical model for aftershock occurrence and rigorously test it against statistical and stress-based models as well as several simple reference models. This new model will retain the important spatial controls that result from the stress perturbation but will circumvent the difficulties associated with the rate-state approach. If successful, we will have a new method for calculating aftershock probabilities.